This project addresses a variety of problems related to protein structure and folding, and uses methods of modern statistical mechanics. Recent rapid advances in experimental techniques for studying protein folding has lead us to concentrate our efforts understanding the physical chemistry of protein folding. We are completing a theory of the nucleation of native structure in protein folding. This work combines the results of a detailed analysis of experimental data with sophisticated ideas in statistical mechanics. We are working with the group of Dr. William A. Eaton of the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) to understand the implications of their experimental results on the kinetics of protein secondary structure formation. To this end we have developed a new mathematical model of alpha-helix kinetics. This new model is explicitly based on the Eaton group's interpretation of their results and it is in the form of a kinetic Ising model, which means that many powerful techniques can be used to investigate the model. In particular, the combination of the experimental results and the analysis of the model can address the long standing question: How much native secondary structure has been formed by the time the protein collapses' In a similar vein, we are developing a theory for the viscosity dependence of protein collapse and folding. This theory will have major implications for the interpretation of protein folding experiments as well as implications for understanding protein folding in the cell and for biotechnology (specifically, for refolding proteins from inclusion bodies).We are continuing work on the determination of the accuracy requirements for potential functions to yield reliable predictions of protein structure. Solution of this problem would give molecular modelers realistic targets for their work and would provide a measure of confidence for a given model. An essential part of this accuracy problem involves the development and exploration of new techniques for incorporating distance constraints into the theory of protein structure. We are completing extensive computer simulations of proteins with distance constraints. These simulations used a theoretical approach that we developed earlier. Without this approach these simulations could not be done, even with the very simple protein models that we used. We are extending this theoretical approach to take into account the stiffness of the protein backbone in a more rigorous manner by using staff (also known as semi-flexible or "worm-like") polymer models in our calculations.In the past year we have verified that a standard technique in statistical mechanics, mean field theory, can be used to calculate important conformational properties of stiff polymers with high accuracy. We plan to apply this technique to stiff polymers with distance constraints and compare the results to recent experiments. We shall also collaborate with Dr. Robert L. Jernigan of the National Cancer Institute (NCI) on investigating the statistics of amino acid contacts in proteins.